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Zbl 0869.60052
Saito, Yoshihiro; Mitsui, Taketomo
Stability analysis of numerical schemes for stochastic differential equations. (English)
[J] SIAM J. Numer. Anal. 33, No.6, 2254-2267 (1996). ISSN 0036-1429; ISSN 1095-7170/e

A linear stability analysis is discussed for numerical discrete time solution methods of Itô differential equations. The function which defines a recursion between the second moments of the approximations in the steps $n$ and $n+1$ is called the stability function of the numerical scheme. A scheme is called mean square stable if the absolute value of the stability function is less than 1. Stability functions and regions are determined for schemes of Euler and Heun type. The paper contains also results of numerical experiments.
[W.Grecksch (Halle)]

MSC 2000:: *60H10 Stochastic ordinary differential equations
65C99 Numerical simulation
65C20 Models (numerical methods)
65L20 Stability of numerical methods for ODE

Keywords: stability of numerical schemes; Ito equations; linear systems

Cited in: Zbl 1042.65013

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